A distillery makes whisky, where its profits from production per bottle are given by 7 = p – y² where p is the price it charges per bottle and y is the number of years the bottle is aged. There are two types of whisky drinkers, connoisseurs (H type) and casuals (L type). H-type have utility UH (Y, p) = 8y - p, while L-type have utility uz (y, p) = 2y – p. There are 10 consumers of each type, and each will buy at most one bottle. Each consumer's utility if she does not buy is 0. If a consumer is indifferent between buying two bottles, assume she will buy the more aged one (the one wi higher y). If a consumer is indifferent between buying a bottle and not buying, assume she will buy. Bottles are characterised by (y, p), years of age and price. For each menu of offerings below, calculate the distillery's profit. (1,9) and (4, 24) (1, 2) and (4, 24) (1, 2) and (2, 24) Calculate the firm's profits when it chooses the optimal menu.

A distillery makes whisky, where its profits from production per bottle are given by 7 = p – y² where p is the price it charges per bottle and y is the number of years the bottle is aged. There are two types of whisky drinkers, connoisseurs (H type) and casuals (L type). H-type have utility UH (Y, p) = 8y - p, while L-type have utility uz (y, p) = 2y – p. There are 10 consumers of each type, and each will buy at most one bottle. Each consumer's utility if she does not buy is 0. If a consumer is indifferent between buying two bottles, assume she will buy the more aged one (the one wi higher y). If a consumer is indifferent between buying a bottle and not buying, assume she will buy. Bottles are characterised by (y, p), years of age and price. For each menu of offerings below, calculate the distillery's profit. (1,9) and (4, 24) (1, 2) and (4, 24) (1, 2) and (2, 24) Calculate the firm's profits when it chooses the optimal menu.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.6P

See similar textbooks

Similar questions

Your own a chocolate producing company which can advertise on both television (T) and internet(I). The effect of TV and online commercials on sales is again given byS(T,I) = 500 + 48T−6T2+ 112I−6I2+ 4TI. You have a budget of $25 that you can spend on T and I. The price of aTV commercial is $12per unit and the price of an online commercial is also $12 per unit. 1. Determine the optimal level of TV commercials T and online commercials I if you have to spend all of your budget. You should provide two methods to solve this, by direct substitution and by setting up the Lagrangian. Is the Lagrange multiplier positive or negative? Give an intuitive interpretation of why this is the case? 2. Now determine the optimal level of TV commercials T and online commercials I if you DO NOT have to spend all of your budget. Do you obtain the same answer as subquestion 5.1? What is the Lagrange multiplier equal to in this case? Discuss.
Think of a person who likes having impact on their social networks. To do so, they always follow the las trends and adapts them to their profile (copies dance moves, open threads, answers DMs, etc.). As their number of followers increase, they are more satisfied. Let us say that this satisfaction is represented by this usefulness function u(f)=f2, where f represents the number of followers. Explain what the law of diminishing marginal returns consists of and if it is complied with in this case. Justify your answer.
6. Exercise 4.6 An econometrician hired to analyse a local golf course has determined that there are two types of golfers, the regular and the occasional. The annual demand for games from regular players is given by QH = 24 - 0.3P, where P is the price of a round of golf. On the other hand, the annual demand for occasional items is given by Q° = 10 - 0.1P. The marginal cost and the average total cost per item are equal to €20. a) If you could distinguish between regular and casual players, what price would be set for each type? How many games would each type of player play? How much profit could the golf course generate? Represent graphically. b) As an alternative to the discrimination of third degree prices, those in charge consider a double tranche rate according to which the members can play as many games as they wish at a price of € 20 per game. How much profit will the golf course generate if it charges all players the same annual fee for becoming a member of the club? What if you…
Brit-Brick is a company that produces bricks and cement in the UK. Their largest consumer is ConstrUK, a UK construction company. The manager of Brit-Brick has asked the research department to find out how sensitive ConstrUK’s demand for bricks is. The research department has estimated that ConstrUK’s preferences over bricks (x) and cement (y) can be described by the utility function U(x,y)=x^(7/10)y^(1-7/10) The price for one bag of cement is equal to £1. It is estimated that ConstrUK’s budget is £10,000. Find the price-consumption curve for bricks and the corresponding demand curve.
Question 9 A computer reseller needs to decide how many laptops to order next month. The lowest end laptop costs $220 and the retailer can sell these for $300. However, the laptop manufacturer already announced that they are coming out with a new model in a couple of months. Any laptops that will not be sold by the end of next month will have to be heavily discounted at half-price. The reseller also needs to consider that every time he fails to fulfill a laptop order, he stands to lose $25 for every unit. Based on the past months’ sales, the reseller estimates the demand probabilities for sales (S) as follows: P(0 units) = 0.3; P(1 units) = 0.4; P(2 units) = 0.2; P(3 units) =0.1. The reseller thinks it’s a good idea to conduct a survey on whether or not his customers are going to buy laptops and how many. The survey results will either be Yes (Y), No (N), or Don’t Know (DK). The probability estimates of the results based on the demand for the number of units are: P(Y|S = 0 units) =…
Brit-Brick is a company that produces bricks and cement in the UK. Their largest consumer is ConstrUK, a UK construction company. The manager of Brit-Brick has asked the research department to find out how sensitive ÇonstrUK's demand for bricks is. The research department has estimated that ConstrUK's preferences over bricks (x) and cement (y) can be described by the utility function - U (x, y) xb/10 y1-b/10 ,- where b =0. The price for one bag of cement is equal to £1. It is estimated that ConstrUK's budget is £10,000. Find the price-consumption curve for bricks and the corresponding demand curve.
k : ces As the manager of Smith Construction, you need to make a decision on the number of homes to build in a new residential area where you are the only builder. Unfortunately, you must build the homes before you learn how strong demand is for homes in this large neighborhood. There is a 50 percent chance of low demand and a 50 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are P= 300,000-400Q and P= 500,000 -225Q, respectively. Your cost function is CQ) = 165,000+ 243,750Q. How many new homes should you build, and what profits can you expect? Number of homes you should build: homes Profits you can expect: $1
Clubs often do some buying and selling during fundraisers, working with a vendor to make mugs, T-shirts, hoodies etc. that display the club's logo. There can be big savings for bulk orders. DiscountMugS (http://www.discountmugs.com) is an on-line company with this kind of service. Suppose a high school group orders T-shirts for a fundraiser. The table below shows the pricing shown on the webslte. Note that the fixed cost Involved in setting up the printing with the logo is absorbed into the pricing schedule. 576+ 1008+ 2016+ Quantity Cost per T S5.55 $4.90 $4.86 12+ 24+ 36+ 72+ 144+ 288+ $4.73 $4.62 $4.58 $4.42 $4.01 S3.59 a) We have seen problems for which breaking even was the goal, but in the context of fundraising the idea of break-even is not really the point! The goal may be to raise enough funds for, say, the choir to take part in an out of state competition, or for the Odyssey of the Mind team to go to World's. If the club is comfortable charging $8 per T-shirt how many must be…
Brit-Brick is a company that produces bricks and cement in the UK. Their largest consumer is ConstrUK, a UK construction company. The manager of Brit-Brick has asked the research department to find out how sensitive ConstrUK’s demand for bricks is. The research department has estimated that ConstrUK’s preferences over bricks (x) and cement (y) can be described by the utility function U(x,y)=xb/10y1-b/10 where b is 2, and where x and y are measured in bags. Example: if b=4, then . U(x,y)=x4/10y1-4/10=x2/5y3/5 The price for one bag of cement is equal to £1. It is estimated that ConstrUK’s budget is £10,000. Find the price-consumption curve for bricks and the corresponding demand curve.
Brit-Brick is a company that produces bricks and cement in the UK. Their largest consumer is ConstrUK, a UK construction company. The manager of Brit-Brick has asked the research department to find out how sensitive ConstrUK's demand for bricks is. The research department has estimated that ConstrUK's preferences over bricks (x) and cement (y) can be described by the utility function U(x,y) = x³/10 y1-b/10 where b=8, and where x and y are measured in bags. Example: if b=4, then U(x,y) = x*/10 yl-4/10 = x2/5 y3/5 The price for one bag of cement is equal to £1. It is estimated that ConstrUK's budget is £10,000. Find the price-consumption curve for bricks and the corresponding demand curve.
Your niece owns a different type of chicken restaurant. She specializes in chicken and noodles and chicken pot pie. Her pot pie is the better seller. However, when its cold outside, the chicken and noodles is the better seller. She goes through about 100 chickens every two days. It takes about 60 chickens to make 600 pot pies. The other 40 chickens are used to make about 320 chicken and noodle dishes. When its cold outside it takes 70 chickens to meet the demand for chicken and noodles. Construct a production possibilities model that graphically illustrates this problem.
Consider the following utility function U(X,Y) = 2X + 3Y PX,PY, and I are exogenous. (a) What is the demand function for X? (b) What is the demand function for Y?